Presidential 2007 Dollar Coin

yep, random - but on proofs they should be the same as the edge gets struck at the same time as the obverse and reverse.

Just to be complete, here is an example labeled as Position A.

Well, Ill be darn. I did not know that. Thanks for the information jbuck and Dearborn.

Dollar coins are struck as a normal coin is, with a plain edge. The coins then drop into a big hopper. At the bottom of the hopper, the coins come out and are fed into the edge-inscribing machine. So it's literally a coin toss, which way around the coins end up landing. As such, there is no "Wrong way up", so they are not an error. They aren't even normally considered a variety; since the Mint carefully designed this process, it is "just how these coins are".

For the proof versions of the coins, as was the case for older edge-lettered coins such as pre-1933 gold, they had the lettering added to the coin by the collar die, at the same time as the coin was struck; such coins do have a "right way up", and having an "upside-down collar die" on those coins would indeed be an error. But for circulation coins, the Mint obviously decided that edge-lettered collar dies would be too slow and expensive for current high-speed production methods.